def GNR_zigzag(Nz):
# create cnt coordinates
cnt = swcnt(((Nz+1)//2,(Nz+1)//2)) # armchair CNT !
minx = Inf
maxx = -Inf
atoms = cnt.atoms[:Nz*2]
# unroll the cnt
for a in atoms:
r = norm(a.pos[:2])
# print a.pos
phi = atan2(a.pos[1],a.pos[0])%(2*pi)
# print phi
a.pos[0] = r*phi
minx = min(minx,a.pos[0])
maxx = max(maxx,a.pos[0])
a.pos[1] = 0
a.rot = asmatrix(eye(3))
for a in atoms:
a.pos[0] -= (maxx+minx)*0.5
res = xyz.chain(period=cnt.period)
res.atoms = atoms
return res
def zigzag(N):
CC_distance = param.GRAPHENE_CC_DISTANCE
period = 3*CC_distance
r = N * 3.**.5 * CC_distance / (2*pi)
res = xyz.chain((0,0,period))
res.radius = r
def addatom(rho,phi,z):
res.atoms.append(xyz.atom('C',
pos=(rho*cos(phi),rho*sin(phi),z),
rot=[[cos(phi),-sin(phi),0],[sin(phi),cos(phi),0],[0,0,1]],
))
for n in range(N):
addatom(r,2*pi*(2*n )/(2*N),period/6)
addatom(r,2*pi*(2*n )/(2*N),period/2)
addatom(r,2*pi*(2*n+1)/(2*N),0)
addatom(r,2*pi*(2*n+1)/(2*N),period/1.5)
return res
def chiral(M,N):
assert M >= 0
assert N >= 0
if M==0:
M,N=N,0
assert M > 0
CC_distance = param.GRAPHENE_CC_DISTANCE
r = radius(M,N)
multiple = gcd(M,N)
multiple_perp = gcd((M+2*N),(2*M+N))
# = gcd(3M+3N,2M+N)
# = gcd(-3M,2M+N)
# = gcd(-3M,-M+N)
# = gcd(3M,M-N)
M_perp = (M+2*N) / multiple_perp
N_perp = (2*M+N) / multiple_perp
period = CC_distance * (3.0 * (M_perp**2 + N_perp**2 - M_perp*N_perp))**0.5
# = CC_distance * sqrt(3.0) * sqrt((M+2*N)**2 + (2*M+N)**2 - (M+2*N)*(2*M+N)) / multiple_perp
# = CC_distance * sqrt(3.0) * sqrt(3*M**2 + 3*N**2 + 3*M*N) / multiple_perp
# = CC_distance * 3 * sqrt(M**2 + N**2 + M*N) / gcd((M+2*N),(2*M+N))
Nplaquettes = 2 * (M**2 + N**2 + M*N)/multiple_perp
Natoms = Nplaquettes * 2
Nlines = (M+N)/multiple
start = [0]*Nlines
stop = [0]*Nlines
for l in range(Nlines):
start[l] = -(l*N/(M+N))
for l in range(Nlines):
stop[l] = N_perp + start[(l-(M_perp-N_perp))%Nlines] - N/multiple*((l-(M_perp-N_perp))/Nlines)
# assert (sum(stop) - sum(start)) * multiple == Nplaquettes
"""
X*a = R*(Ma+Nb)+L*((M+2N)a-(2M+N)b)
b: 0 = RN-2LM-LN
R = 2LM/N+L
a: X = (2LM/N+L)M+LM+2LN
L:=N
R = 2M+N
X = 2MM+2NM+2NN
"""
dphi_a = 2*pi * (2*M+N)/(2*(M*M + M*N + N*N))
dphi_b = 2*pi * (M+2*N)/(2*(M*M + M*N + N*N))
dphi_c = dphi_a - dphi_b
dz_a = CC_distance * sqrt(3) * sqrt((2*M+N)**2 + (M+2*N)**2 - (2*M+N)*(M+2*N)) * N / (2*(M*M + M*N + N*N))
dz_b = - CC_distance * sqrt(3) * sqrt((2*M+N)**2 + (M+2*N)**2 - (2*M+N)*(M+2*N)) * M / (2*(M*M + M*N + N*N))
dz_c = dz_a - dz_b
res = xyz.chain((0,0,period))
res.radius = r
def addatom(rho,phi,z):
res.atoms.append(xyz.atom('C',
pos=(rho*cos(phi),rho*sin(phi),z),
rot=[[cos(phi),-sin(phi),0],[sin(phi),cos(phi),0],[0,0,1]],
))
n = 0
for l in range(Nlines):
for p in range(start[l],stop[l]):
for m in range(multiple):
phi_A = dphi_a * l + dphi_c * p + 2*pi*m/multiple
z_A = dz_a * l + dz_c * p
phi_B = phi_A + (dphi_a+dphi_b)/3
z_B = z_A + (dz_a+dz_b)/3
addatom(r,phi_A,z_A)
addatom(r,phi_B,z_B)
assert len(res.atoms) == Natoms
return res